# Is there such a thing as resonance in economic underliers?

In physics the occurence of resonance is explained and widely understood in its linear form and subject to research in nonlinear resonance.

Example for instance are resonant frequencies of objects.

Now it is not so much of a stretch of imagination to look for resonance in economic times series.

Correlation is only a linear measure of linking time series and it doesnt explain the mechanism for resonance.

Can we explain selloffs and squeezes by resonant interactions of a complex system and is it possible to detect resonance in stock price time series of multiple stocks?

• It's hard to find something like a "natural frequency" in the time series of a tradable asset. If it existed, it would allow for making big profits by buying bottoms and selling tops, which would lead to nullify such frequency. – Lisa Ann Mar 30 '19 at 14:15
• There doesn’t need to be a single natural frequency to do so. In fact it could be that there are an infinite number of eigenfunctions corresponding to eigenfrequencies. Maybe even the eigenfunctions don’t correspond to a single set of type of function either. I am just wondering how one could approach this. There are equation free models that will give you a spectrum of Eigenvalues real and imaginary and maybe in the Modulation of these eigenvalues it is possible to deduce resonance at times of extreme selloffs for instance? – AndiAna Mar 30 '19 at 18:14

I would argue as follows: In order to observe any type of resonant behaviour, the dynamics of the system you are looking at needs to be described by a second order differential equation. The equations of motions that come to mind in economics are clearly not:

GBM: $$dS=\mu S dt+\sigma S dZ$$

OU: $$dX=\theta(\mu - X)dt+\sigma dW$$

• Yes I see that would all be linear. You would need to be able to deduce a wavelength wavenumber equation. But with nonlinear resonance it is not necessarily the requirement...? What is the process causing a peak in signals at times of extreme selloffs ? I know that correlation is just one variable to measure but the instantaneous correlation is not possible to calculate. What is the reason behind a rapid increase in signals (TA) around selloffs or sharp rises? It is similar in nature to resonance since the same pattern starts to appear in a multitude of seemingly independent variables... – AndiAna Mar 30 '19 at 18:20
• ultimately you will have to pick a set of driving variables, come up with a "physical" mechanism of how they change prices and then statistically test the validity of your hypothetical mechanism. i am intensely curious :) – ZRH Mar 30 '19 at 20:08
• yes i keep asking, its kind of like negentropy. which is the deviation from a normal distribution. negentropy (as opp. to entropy) is high when suddenly information is high. when information is random negentropy is low. this is very likely what is happening. in that each TA signal on its own is more or less random but when you have a sudden increase in negentropy your TA signals start to coincide and the concentration of signals becomes suddenly mutiples of standard deviations like 6-7 sigma events. but you are asking the right question: what is the mechanism? which are the driving variables? – AndiAna Mar 30 '19 at 20:31